Orbital rates of earth satellites at resonances to test the accuracy of earth gravity field models

Abstract

Differences among the Earth gravity field models, which were (in Klokočník and Pospíšilová, 1981) expressed as dispersions of the relevant lumped geopotential coefficients, are here transformed to the differences in variations of orbital quantities.

Theoretical formulae, the Lagrange (planetary) equations, describing the orbital rates near resonances due to the geopotential, are derived in a simple and unified form. They are then applied to estimate the orbital uncertainty as a function of Earth models differences. The first set of the Earth models (set I) consists of 11 models from the decade 1970–1980, of greatly varying quality; the set II contains several recent models; we present a test (for the 13th-to 15th-order) based on standard deviations of the lumped values of GEM 10B, which were estimated by means of independent resonant data (in Klokočník, 1982).

Maxima of the differences in the variations of the elements for the set I reach 8×10⁻⁴ deg day⁻¹, 10–12 m day⁻¹ or 200 m day⁻¹ inI, a, orL ₀=ω+M ₀+Ω, respectively, for close and polar orbits (∼15 revs day⁻¹); the values are not higher than 10⁻⁴ deg day⁻¹, 1–2 m day⁻¹ or 20 m day⁻¹ inI, a,L ₀ for higher orbits (∼6–7 revs day⁻¹). For the set II, calibrated by resonant data, the maximum inaccuracy (±3σ) is about 3×10⁻⁴ deg day⁻¹, ≤6 m day⁻¹ or ≤100 m day⁻¹ forI, a, andL ₀ at 15 revs day⁻¹, and is not larger than∼1×10⁻⁴ deg day⁻¹, 2 m day⁻¹ or 25 m day⁻¹ for 13 revs day⁻¹.